STUDIES IX T H E PHYSICAL CHEMISTRY OF AMINO ACIDS, PEPTIDES, AND RELATED SUBSTANCES. XI1
INTERACTIONS BETWEEN DIPOLARIONS
IN
AQUEOUSSOLUTION'
EDWIN J. COHN, T. L. McMEEKIN, JOHN D. FERRY, AND MURIEL H. BLANCHARD Department of Physical Chemistry, Harvard Medical School, Boston, Massachusetts Received October I d , 1958 I. INTRODUCTION
The class of molecules whose interactions we are considering here is characterized by having a t least one positively charged and one negatively charged group in the neutral isoelectric state. Under these circumstances they do not move with the current and are therefore not ions in the sense of Faraday. They are, however, oriented by an electric field by virtue of their large dipole moments and may for convenience be called dipolar ions. The simplest dipolar ion is glycine or aminoacetic acid. (Carbamic acid-aminoformic acid--does not exist in the free state in aqueous solution, although certain of its salts are stable.) It contains a positively charged NH: group and a negatively charged COO- group, sepaorated by a CH2 group. The distance of separation is something over 3 A. and the dipole moment therefore approximately 15 Debye units. Other dipolar ions may differ from glycine by the number of NH: groups, of COO- groups, or of CH2 groups. The latter may increase the distance of separation between the positively and negatively charged groups, and therefore the dipole moment of the molecule, or this may remain the same, as in all a-amino acids which differ from each other in the length and configuration of their paraffin side chains. Dipolar ions may, however, contain still other groups. Thus amino acids bound to each other in peptide linkage contain one or more CONH groups, and the moments of di- and tri-peptides are greater than those of the simple amino acids. Peptides may also have paraffin side chains, sulfhydryl or hydroxyl groups, or other configurations possessed by the amino acids of which they are constituted. Regardless of the complexity of their structure, the balance between two phenomena would appear to determine their behavior. Dipolar ions that Presented a t the Symposium on Intermolecular Action, heldat BrownUniversity, Providence, Rhode Island, December 27-29, 1938, under the auspices of the Division of Physical and Inorganic Chemistry of the American Chemical Society. 169
170
COHN, MCMEEICIN, FERRY AND BLANCHARD
are small in comparison with their moments have lower activity coefficients in more concentrated solutions. I n this they resemble most ions. The resemblance goes further, for the effect upon the activity coefficient is smaller per mole the higher the concentration. Dipolar ions whose volumes are large in comparison with their moments generally have activity coefficients that are greater than unity. Moreover, the logarithm of the activity coefficient is essentially linear in the concentration. In this the behavior of such dipolar ions resembles that of many uncharged molecules. The ratio of moment to volume thus renders the behavior of dipolar ions more comparable on the one hand to that of ions and, on the other, to that of uncharged molecules. This dichotomous behavior applies not only to the interactions of dipolar ions with each other but also to their interaction with ions. In early studies upon the solubility of amino acids in salt solutions (24, 23, 10) it was noted that neutral salts dissolved some amino acids and precipitated others. Among those dissolved was glycine; among those precipitated were leucine and tryptophane,- large amino acids which were “salted out.” These solvent and precipitating actions of neutral salts had been noted with respect to the interaction of neutral salts and proteins long before they were noted for neutral salts and the amino acids of which proteins are constituted. In 1856 Denis noted that a fraction of the protein in blood was soluble in dilute salt solutions but not in water. In 1887 Hofmeister studied extensively the “salting-out” of proteins by electrolytes. These effectsof salt are far greater in the case of proteins than of smaller dipolar ions and were therefore observed earlier. I n order, however, to understand the nature of the molecular configurations which lead to changes in the activity coefficients of dipolar ions, we shall consider first smaller molecules of known structure. 11. SYSTEMS CONTAINING GLYCINE
Glycine The influence of glycine in lowering the freezing point of aqueous solutions has been accurately investigated by Scatchard and Prentiss (28). Their results, calculated as activity coefficients a t the freedng point, are given by the relation -logy = 0.09910m - 0.01584m2 (1) where m is concentration per 1000 grams of water. By means of the heat capacity and heats of dilution of Zittle and Schmidt (34) the above relation? calculated by Scatchard for 25OC., yields -logy = 0.08366m - 0.01507m2
(2)
3 Gucker is investigating the heat capacities and the heats of dilution of glycine, alanine, and of certain related moleculee, and his results when completed should lead to slight revision of these values.
INTERACTIONS BETWEEN DIPOLAR IONS
171
The activity coefficients of glycine have also been determined by vapor pressure measurements by Smith and Smith (30) and by M. M. Richards (26), and their results are in good agreement as a first approximation3 with the freezing point determinations of Scatchard and Prentiss (28), with which they are compared in table 1. TABLE 1 Activity cs @cients of !ycine i n a ieous solution at 86°C.
--
QLTCINE CONCEKTRATION
DIELBmRIC CONSTANT
D
m
l
C
molcr pcr
molrr p a
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1.0 1.2 1.4 1.5 1.6 1.7 1.8 2.0 2.2 2.4 2.5 2.6 2.8 3.0 3.2 3.3
0.099 0.198
IWOurama
-LOQ 'I (SMITE AND SMITE (301, R Y VAPOR PREBIJURE)
-LOQ r (RICHARDS BY VAPOR
PRESSURE)
-LOQ r (CATCHARD W D PRENTISS
%),*BY men
- L o a 'I (CALCULATEDt)
INQ POINT)
2ifa
0.296
0.393 0.489 0.585 0.679 0.773 0.958 1.140 1.318 1.406 1.494 1.580 1.666 1.836 2.002 2.166 2.247 2.327 2.485 2.640 2.793 2.869
80.8 83.0 85.2 87.4 89.6 91.7 93.8 96.0 100.1 104.2 108.3 110.3 112.2 114.2 116.1 120.0 123.7 127.5 129.3 131.1 134.7 138.3 141.8 143.5
0.0088 0.0168 0.0241 0.0315 0.0386
0.0177 0.0330
0.0082 0.0161 0.0237 0.0310 0.0381
0,0463 0.0516 0.0685 0.0768
0.0512 0.0681 0.0686$ 0.0780 0.0865
0.0883
0.0686 0.0787
0.0863
0.0916 0.0941
0.0964 0.105
0.0987 0.1009 0.107 0.113 0.119
0.119 0.130
0.124 0.128 0.133 0.136
0.137
* Calcdated for 25°C. by means of equation 2. t Calculated by means of the equation: -(logy)/C
= K:
0.0089 0.0173 0.0252 0.0326 0.0395 0.0460 0.0521 0.0578 0.0684 0.0780
0.107
0.0903 0.0939 0.0976 0.101 0.107 0.113 0.118 0.121 0.123 0.128 0.132 0.135 0.137
(Do/D) - K:, where K:
= 0.100 and K: = 0.007.
$ This value is aeaumed equal to that of Scatchard and Prentiss at the same temperature and concentration (see reference 26, page 733).
There are several qualitative observations that may be made regarding t.hese data: (a)as in the case of most electrolytes, the activity coefficients are less than unity; (b) unlike the case of electrolytes, -log y varies in See second footnote to table 1.
172
COHN, MCMEEKIS, FERRY AND BLANCHARD
dilute solution with C and not with its square root; and ( c ) the ratio - (logy)/C does not remain constant but diminishes with increasing concentration. Glycine and asparagine Glycine cannot be investigated in aqueous solutions by the solubility method. Most other a-amino acids are less soluble, but their paraffin side chains introduce strong repulsive forces to be considered subsequently. Asparagine is, however, an a-amino acid of low solubility and with no exposed CH2 group. bioreover, the terminal group contains the CONH group, characteristic of the peptide linkage. Ammonia can be split from this group of asparagine and of the closely related glutamine in acid solution (1, 25), and the concentration of these amides in systems containing other amino acids can thus readily be investigated either by titration or by Nessler determination of the liberated ammonia. The purification of asparagine offers some difficulty, as has been noted by several investigators (see, for instance, reference 29, page 489). Aspartic acid is usually present as an impurity and is best removed by carrying out the crystallizations at pH 6. Under these conditions salts of aspartic acid that are either present or fornied during the processes of purification remain in the filtrate. The asparagine used in these experiments was crystallized once from water and twice from 50 per cent ethanol. ;ifter drying in a desiccator to constant weight, it contained one niolecule of water of crystallization. A saturated aqueous solution had a pH of 5.4, which is close to the isoelectric point as calculated from the dissociation constants, and the conductivity was 7 x reciprocal ohms. Our preparations gave the theoretical value for amide nitrogen, namely, 9.33 per cent. The solubility of asparagine was determined by the method of Pucher, Vickery, and Leavenworth (25). It was found necessary to increase the time of heating in acid to 20 hr. under the conditions of our experiments. Following our usual procedure (6) , analyses were made after successive equilibrations of solrcnts n ith asparagine for approxiniately 24 hr. until the saturated solutions gave the sanie solubility for a t least three successive days. Most amino acids increase the solubility of asparagine, and the activity coefficients of the asparagine calculated from such nieasurcmcnts are given in table 2. The aolubility increased from 0.184 mole per liter in water to only 0.192 in 1.5 molal alanine and decreased to 0.170 inole per liter in 1 . 5 molal a-aniinobutyric acid. The greatest change in solutions of these two amino acids thus never exceeded 5 per cent, or approximately ten times the experimental error, whereas the same concentration of gl) cine increaqcd solubility by more than 20 pcr cent The rcqultu relating glycine
,
173
INTERACTIONS BETWEE?; DIPOLAR 10x6
and asparagine have been plotted in figure 1 and compared with the \-arious studies by freezing point and rapor pressure methods of the actiyity coefficient of glycine. TABLE 2
Solubilitu of 1-asparaqine in aqueous amino acid solitlions at 25°C
'
moiea per liter
00
~
1.50 2.00 2.80
1 00711
1.05383 1.06861 1.09080
1
1
,
!-Asparagine in water 78 5
112.4 123.7 141.8
moles per liter 1 molefroclion
1 ~
l-Asparagine in diglycine. 6 25
i
0 50 loo 1 40
1
o
1
1 1 1 1
02164 03508 1 06120 08170
96 2 113 8 149 1 177 4
0 184
0 00336
0.225 0.231 0.247
0.00430
=
I
1.01762 1.02780
I
112.4 144.8
0 218 0 221
~
i
I-Asparagine in alanine. 6 0 25
1 01436
1 02132 1 03490
1
84 2 89 8 101 1
'1
150
1 01382 1 02025 1 03347 1 01591
~
I
I
34 2 39 8 111 1 112 4
1
1
,
345; I/C of approximately 0.07 m y be expected for each nonpolar CHZgroup in parafin side chains. Opposite in direction to the effect of paraffin side chains, in diminishing
' Hemoglobin exhibits this effect in the most concentrated glycine solutions (26).
180
COHN, MCMEEKIN, FERRY AND BLANCHARD
TABLE 3 Solubility of cystine in aqueous amino acid solutions at 86°C.
Cystine in water
1
molar per liW
0.0
0.9972
1
1
j
molcr per liter
78.5
i
I
mdcfrllction
i
0.000454 10.00000820
glycine. 6 = 22.6;K R = 0.293;K , = 0.007
1.0020 1.00512 1.01279 1.02801 1.0422 1 ,05755 1 ,08033
0.1 0.25 0.5 1 .o 1.5 2.0 2.8
80.8 84.2 89.8 101.1 112.4 123.7 141.8
0,000478 0.000518 O.OOO558 0.000632 0,000701 0.000743 0 . 000779
0.00000865 0.00000942 0 . oooO102 O.ooOo117 O.ooOo132 0 . oooO142 O.oooO152
0.023 0.060 0.095 0.154 0.207 0.238 0.268
0.022
0.052 0.095 0.161 0.207 0.238 0.267
-
Cystine in diglycine. 6
0.25
1.01097
0‘5 1.4
::?:
=
70.6;K R = 0.380;K , = 0.0
I :;A 1 1 96.2
0.000532 0.00000976 0.000597 O.oooO111 0.000711 O.oooO140
Cystine in urea.* K R = 0.085;K ,
1 .o 2.0
0.25 0’5 1 .o
~
1.0133 1.02852
1
81.3 84.0
I
1
=
’ ~
:::::1 ::::; 0.075
0.0
!
0.000536 0.00000994 0.000622 O.oooO119
0.083
0.162
0.078
I
0.082 0.156
1
0.033
Cystine in dl-alanine. 6 = 22.6;KR = 0.593;K , = 0.136
1 1 1 1.00431 1.01139 1.02529
84.2
1:;:;
0.000495 0.000009041 0.042 0.000513 0.00000947 0.062 0.000532 ~O.oooO1004 0.088 ~
’
1
0.060
0.092 -
Cystine in a-aminobutyric acid. 6 = 22.6;K R = 0.293;K. = 0.191
0.25 0.5 1 .o 1.5
0.25 0.5
1
0.000474 0.000475 0.000461 0.000442
84.2 89.8 101.1 112.4
1.00408 1.01082 1 ,02435 1 ,03764
Cystine in dl-valine. 6
1.00382 1.01046
1
84.2 89.8
1
=
0.00000881
0.00000884 0. ooOOO875
22.6;h r ~= 0.293;K, = 0.234
1
0.000454 O.oooO0835 0,000453 0.00000849
* Values for D are taken from Wyman
0.021 0.033 0.037 0.021
0.025 0.032 0.032 0.028
0.00000869
~
0.008
0.015
1
0.010 0.011
(32).
the interactions between dipolar ions in aqueous solution, is the influence of their electric moments. For cystine, as for asparagine, the solvent action is greater for diglycine than for glycine. For urea, with a moment of
181
INTERACTIONS BETWEEN DIPOLAR IONS
approximately 5.1 Debye units (9), the very definite solvent action is less than for glycine. Moreover, as a first approximation the change in free energy of interacting dipolar ions without parafin side chains would appear to be proportional to the first power of their moments. VII. DISCUSSION
In considering the influence of various solvents upon the change in free energy of dipolar ions we have previously employed ( 6 ) the extensions of Debye’s treatment for ions to the case of dipolar ions of Scatchard and Kirkwood (27) and of Kirkwood (16). Whether the shape of the dipolar ion be considered to be that of a dumb-bell, of a sphere, or of an ellipsoid, it appears that an additional term is required to account for the influence of the various groups of the dipolar ions. The change in free energy due to electrostatic forces ( P , -- p:) can be estimated from the observed activity coefficients, even as a first approximation, only after correction for the effects of these groups. An equation wa5 therefore tentatively adopted with the form ( 6 )
P, -
(log N/No - K,) = K Z( l / D
= -2.303kT
- 1/Do)
(3)
in which K1 is a constant related to non-electrostatic forces. K1 has been shown to increase in series both of a-amino acids and of hydantoic acids for each additional CH2 group in paraffin side chains ending in methyl groups by 0.23 for the transfer from water to formamide, by 0.44 t o methanol, by 0.49 to ethanol and acetone, and by 0.53 t o butanol and heptanol (3, page 245). If the values for K1 be divided by the numbers of moles per liter in the pure non-aqueous solvents, these increments for each additional CH2 group become 0.0092 for the transfer to formamide, 0.0179 to methanol, 0.0287 to ethanol, 0.0362 to acetone, 0.0487 to butanol, and 0.0751 to heptanol. If we multiply ( 1 / D - 1/DO) by - D i / 6 , we have -(Do’/h)(llD
- l/Do)
= ( D o / D ) ( D - Do)/6
(4)
The quantity 6 in the above expression is the dielectric constant increment, defined by the relation 6 = ( D - Do)/C, which has been proven to hold for most dipolar ions by Hedestrand (15),Devoto (8), Wyman and Mchfeekin (33), and others. For the interaction between dipolar ions it will be more convenient to substitute for ( D - DO)/^ in the last equation the concentration, C, in moles per liter of the dipolar ion. The change in free energy due to electrostatic forces can therefore conveniently be written for interactions involving dipolar ions in the form
- ( F e - Fz)/2.303kT
=
log N / N o
+ K f C = Ki(Do/D)C
(5)
182
COHN, McMEEKIN, FERRY AND BLANCEARD
in which the salting-out constant K : is equal to
- KJC
and
K;f,= K26/2.303D;kT On the basis of the above equation the logarithm of activity coefficients between dipolar ions should be linear in (Do/D)Cin cases where the salting-
03
0.7
I
FIQ.3. Plot of -(logr)/C against Do/D. 0,hemoglobin (Richards); 0 ,cystine; 8 , glycine (Richards); Q , glycine (Scatchard and Prentiss); 0 , glycine (Smith and Smith); 0 , alanine (Smith and Smith); 8 , a-aminobutyric acid (Smith and Smith). out term is small. This .is closely true for the interaction between asparagine and glycine (table 2) and between cystine and &glycine (table 3). In other cases, if this equation be valid and (log N / N o ) / C be plotted as ordinate against D o / Das abscissa (figure 3 ) , extrapolation to the point where D o / D equals unity should yield ( K i K:). The difference
-
1
183
INTERACTIONS BETWEEN DIPOLAR IONS w e e
t-
0 0 0 0 0
$9%1%1$ W3 9
n~rnnrn
ec?eee
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
gggq 0 0 0 0
$388 0 0 0 0
000000
n w m m n
4c?'944 0 - w o o
-~ .. .. .. .. .. .. .. .. .
.. ...
.. ...
.. ...
.. ...
.. ...
..: ..: .. : .. :0 3. :
184
COH“, MCMEEICIN, FERRY AND BLANCHARD
between this value and that where* Do/D equals 0.5 should yield K i / 2 . In this way estimates of K i and K. for each interaction can be obtained, provided the experimental points fall on a straight line when plotted in this manner. Certain of the measurements reported are analyzed in this way in the final two columns of table 4. The limiting value of the slope, -(log r ) / C , a t zero concentration is conveniently given by K; - K : . Theoretical calculations Scatchard and Kirkwood have extended the treatment for the change in free energy with change in dielectric constant of the solvent to the case of dipolar ions (27). Considering a dipolar ion as made up of two spheres of radius b separated by a distance R , with a charge ez in one sphere and -ez in the other, they evaluate ( P , - E ) / ( I / D - l/Do) as Ne2z2 (l/b - I/R). If we assume the last expression gives K2 in equation 3, or 2.303Di kTKA/G, where Kk is analogous to the experimental K; in equation 5, then when the solubility of a given dipolar ion is influenced by different substances, KA should increase directly with the dielectric constant increment, 6. In order to test this equation we have tentatively assumed that R for glycine and all a-amino acids is 3.17 A. Considering glycine to be a sphere of radius 2.82 A. and the center of the dipole to be a t the center of the molecule, the charges would be 1.24 A. from the edge of the molecule (3, page 264). Taking b as 1.24A. throughout, values of KA, estim.ated on this “dumb-bell model,” are given in column 6 of table 4. This model does not allow for the volume occupied by parts of the molecule not situated between the charged groups. Kirkwood has developed a spherical model (16) within which any number of charges is located. The general expression for the change in free energy with the dielectric constant of the medium is in the form of an infinite series. However, for the special case of two charges equidistant from the center, an explicit summation has been made (2, equation 21). Taking the values of the radius b, given in column 3 of table 4, and assuming the distance of the charges from the edge to be 1.24 A., as before, values of KA have been calculated* and listed in column 7. Here too KA should, according to the theory, be proportional to 6 . I n both these theoretical treatments the dipole molecules whose activity coefficients are considered are supposed to be surrounded by a structureless dielectric continuum, in which the presence of other dipolar ions increases the dielectric constant, their molecular structure being ignored. This picture may be replaced by one somewhat more detailed, which considers 8 For hemoglobin the two charges were taken as L and -23, respectively, consistent with the dipole moment of 500 (22) and R = 51.6 A. (see Ferry, Cohn, and Newman: J . Am. Chem. 900.80, 1480 (1938)).
INTERACTIONS BETWEEN DIPOLAR IONS
186
molecular interaction of pairs of dipolar ions immersed in a supposedly continuous medium with the dielectric constant of the pure solvent. Here the greater complexity of the treatment has led to a simpler model for the dipolar ion. In the development of Fuoss (11, 12) the molecule is represented by a sphere of radius b with a point dipole a t the enter.^ Following FUOSS, the interaction constant of a dipole species i in the presence of an excess of a species k in water at 25OC. is given by
KR = - ( l O g r i ) / C k = 3.69
x
lo-'pipd(z)
where p i and pk are the moments of the two dipoles in Debye units and e(z) is a function given by Fuoss (12, table 2), where X
= 0.706pipk/(bi
f
and bi and b k are the radii of the two dipoles. Here both x and K R , as given by Fuoss, have been multiplied by the factor 9/4, in accordance with the correction of Kirkwood ( 1 7 , 18) for'the case that the dielectric constant of the cavities represented by the molecules is small compared with that of the surrounding solvent. Dipole interaction has been calculated by means of the above equation for the molecules that have been investigated, using the values of p and b given in table 4. These values of Kg are listed in column 8. I n order to account for the salting-out effect in dipole-dipole interaction, Kirkwood (18) has suggested for the same spherical model an equation of the form
which for water a t 25°C. becomes Values of K. calculated on the basis of this equation are listed in column 9, and the .differences KR - K., representing theoretical limiting slopes, are in column 10 of table 4.1° Comparison of theory with experiment These various calculations may now be compared with the experimental limiting slopes in column 11 of table 4. The only cases in which there is 0 This simple model may be also used in the calculation of the change of free energy with dielectric constant; it yields values of Kk somewhat smaller than those in column 7, owing to suppression of terms in the multipole moments which are included in the two-charge model of Kirkwood. l o An alternative molecular model suggested by Kirkwood (la) for calculations of interaction of elongated dipoles is that of a rod joining two charges. The interaction constant KR for water a t 25°C. is 0.167% (1 - R2/3R1), where RI and Rn are the larger and smaller dipole distances, respectively, of the two species of dipolar ions. This yields for KR a value of 0.35 for all a-amino acids,-a figure far.higher than estimated
186
COHN, MCMEEKIN, FERRY AND BLANCHARD
even approximate agreement with the Born-Fajans treatment are those of cystine in urea and hemoglobin in glycine. In each of these systems the molecule whose solubility is measured is large compared with the other dipolar ionic species, so that the merging of the latter in a continuous medium, assumed by the theory, is more closely approached. I n all other systems investigated the calculated values are many times larger than those observed, the discrepancy being greater for the dumb-bell than for the spherical model. Corrected or uncorrected for the salting-out effect, the model for interaction between spherical molecules with dipoles a t their centers gives far smaller results, more nearly of the order of the experimentally observed limiting slopes (column 11). Two types of discrepancy are apparent. For the activity coefficients of glycine, asparagine, cystine, and hemoglobin in glycine, diglycine, and lysylglutamic acid, the calculated limiting slope is too small; presumably the dipoles are mutually accessible to a greater extent than represented by the model. On the other hand, for the activity coefficients of a-amino acids with p a r a f i side chains and for asparagine in a-aminobutyric acid, the calculated limiting slope is too large; presumably the repulsive effect of the side chains is greater than the model represents. While the agreement of the different theoretical approaches with experiment is nowhere satisfactory, the nature of the discrepancies suggests that a much better representation of the facts may be obtained by extending the treatment of dipole-dipole interaction to molecular models of a more detailed and specific structure. Conclusions from experiments The experimental data give the opportunity of making certain further generalizations. Thus the observed activity coefficients are in some cases less, in others greater, than unity. Those calculated (columns 6 to 10) are, however, all less than unity regardless of which model is considered, except in the case of cystine in urea (column 10). Here, however, the observed limiting slope is positive and is given satisfactorily as a first approximation, as we have seen, by the Born-Fajans treatment. Thus the activity coefficients of alanine, a-aminobutyric acid, and a-aminovaleric acid are most readily described in terms of the salting-out constant K:, having the values listed in the last column of table 4. Large values of K: have been observed in all interactions in which one or both dipolar ions have paragin side chains, and the values of K: are, moreover, of the same order of magnitude as for the transfer to non-aqueous solvents. In contrast to the influence of the paraffin side chain upon K: is that of an amide or peptide group. We have estimated that Kr was close to zero in the interaction between glycine and asparagine on the basis of
INTERACTION8 BETWEEN DIPOLhR ION8
187
equation 5 , and asparagine has an amide group. K: has also been estimated to be zero for the interaction of diglycine and cystine, and diglycine contains the peptide linkage. In the interaction between asparagine and diglycine, or asparagine and lysylglutamic acid, where amide and peptide groups are constituent parts of both interacting dipolar ions, K: appears to have a sign opposite to that observed for the other dipolar ions investigated. This is reminiscent of studies upon such molecules as succinic acid (19), for which a linear relationship between “salting-in” by certain electrolytes and the concentration has been observed. The moments for glycine, diglycine, and lysylglutamic acid are 15, 26, and 59 Debye units, respectively. The observed limiting slopes for the interaction of asparagine with these three dipolar ions may be taken as 0.10, 0.17, and 0.23. Thus K i increases by less than the first power of the moment. The interaction of cystine has been studied with urea, glycine, and diglycine, and their moments may be taken as 5.1, 15, and 26, or roughly as 1 is to 3 is to 5. The observed limiting slope for urea, 0.088, is less than a third smaller than that for glycine, and that for diglycine, 0.380, is less than five times that for urea. As in the case of interactions with asparagine, interactions between the dipolar ions that have been investigated indicate that change in free energy with change in moment increases by slightly less than the first power of the products of the moments. VIII. SUMMARY
1. Interactions between dipolar ions in aqueous solution are considered. 2. The activity coefficients of glycine in aqueous solution are approximately given by the equation
- (lOgy)/C
=
K$(Do/D) - K:
where K i = 0.10 and K: = 0.007 a t 25’C. 3. The activity coefficients of a-amino acids with paraffin side chains are all greater than unity, and are given by the equation where K : is equal to 0.011 for alanine, 0.043 for a-aminobutyric acid, and 0.047 for a-aminovaleric acid. 4. The activity coefficients of asparagine, an a-amino acid whose side chain terminates in an amide group, are less than unity in solutions of the other amino acids and peptides studied. In glycine K i , in the above equation, is 0.094, and K , is - 0.006; in diglycine and peptides of larger moment, though K i is greater, K: also appears to be negative. 5. The double dipole, cystine, has both a larger moment and a larger volume than the other a-amino acids investigated, and its activity coefficients in glycine are given by putting K i equal to 0.293 and K : to 0.067.
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COHN, MCMEEKIN, FERRY AND BWNCHARD
In the presence of other dipolar ions K i is greater if their dipole moment is greater, and K : is greater if they contain paraffin side chains. 6. In the interactions of cystine and other dipolar ions, K i appears to vary more nearly with the first than with the second powef of the moment. 7. The observed limiting slopes are compared with calculations based on various models for dipolar ions. REFERENCES (1) CHIBNALL, A. C., AND WESTALL, R. G.: Biochem. J. 26, 122 (1932). (2) Corn, E. J.: Ann. Rev. Biochem. 4,93 (1935). (3) COHN,E.J.: Chem. Rev. 19, 241 (1936). (4) COHN,E. J., MCMEEKIN,T. L., AND BLANCHARD, M. H.: Compt. rend. tra-f. lab. Carlsberg, Sarensen Jubilee Volume, 22, 142 (1938); J. Gen. Physiol. 21, 651 (1938). (5) COHN,E. J., MCMEEKIN,T. L., EDSALL,J. T., AND BLANCHARD, M. H.: J. Am. Chem. SOC.66,784 (1934). (6) Corn, E. J., MCMEEKIN, T. L., EDSALL, J. T., AND WEARE,J. H.: J. Am. Chem. SOC.66, WO (1934). (7) DANIEL,J., AND COHN,E. J.: J. Am. Chem. SOC. 68,415(1936). (8) DEVOTO,G.: Gam. chim. ital. Bo, 520 (1930); 61, 897 (1931); Z. Elektrochem. 40, 490 (1934). (9) DEVOTO,G.: Gam. chim. ital. 83, 491 (1933). (10) EULER, H. VON, AND RUDEERG, K.: z. physiol. Chem. 140, 113 (1924). (11) Fnoss, R. M.: J. Am. Chem. SOC.66, 1027 (1934). (12) Fnoss, R. M.: J. Am. Chem. SOC.68,982 (1936). (13) GREEN,A. A.: J. Biol. Chem. 96, 47 (1932). (14) GREENSTEIN, J. P., AND WYMAN, J., JR.: J. Am. Chem. SOC.68,463 (1936). (15) HEDESTRAND, G.: Z.physik. Chem. 1915, 36 (1928). (16) KIRKWOOD, J. G.: J. Chem. Phys. 2, 351 (1934). (17) KIRKWOOD, J. G.: Chem. Rev. 19, 275 (1936). (18) KIRKWOOD, J. G. : Personal communication. (19) LINDERSTR~M-LANG, K.: Compt. rend. trav. lab. Carlsberg 16, No. 4 (1924). (20) MCMEEKIN,T. L., COHN,E. J., AND WEARE,J. H.: J. Am. Chem. Soa. 67, 626 (1935);68, 2173 (1936). (21) MCMEEKIN,T. L., Corn, E. J., AND BLANCHARD, M. H.: J. Am. Chem. SOC.69, 2717 (1937). (22) ONCLEY, J. L.: J. Am. Chem. SOC.80, 1115 (1938). (23) PFEIFFER,P., AND ANGERN, 0.: Z. physiol. Chem. 199, 180 (1924). (24) PFEIFFER, P., AND WURGLER, J.: Z. physiol. Chem. 97, 128 (1916). (25) PUCHER, G.W.,VICKERY,H. B., AND LEAVENWORTH, C. S.: Ind. Eng. Chem. 7, 152 (1935). (26) RICHARDS, M. M.:J. Biol. Chem. 122, 727 (1938). (27) SCATCHARD, G., AND KIRKWOOD, J. G.: Physik. Z. SS, 297 (1932). (28) SCATCHARD, G.,AND PRENTISS, S. S.: J. Am. Chem. SOC.66, 2314 (1934). (29) SCHMIDT, C. L. A.: The Chemistry of the Amino Acids and Proteins. Charles C. Thomas, Springfield, Illinois (1938). (30) SMITH,E. R. B., AND SMITH,P. K.: J. Biol. Chem. 117, 209 (1937). (31) SMITH,P.K., AND SMITH,E. R. B.: J. Biol. Chem. 121, 607 (1937). (32) WYMAN, J., JR.: J. Am. Chem. SOC.66, 4116 (1933). (33) Wmm, J., JR., AND MCMEEKIN,T. L.: J. Am. Chem. SOC. 66, 908 (1933). (34) ZITTLE, C. A,, AND SCHMIDT, C. L. A , : J. Biol. Chem. 108, 161 (1935).
